Synchronization of a genetic oscillator with the cell division cycle

Abstract

Genetic circuits that control specific cellular functions are never fully insulated against influences of other parts of the cell. For example, they are subject to periodic modulation by the cell cycle through volume growth and gene doubling. To investigate possible effects of the cell cycle on oscillatory gene circuits dynamics, we modelled a simple synthetic genetic oscillator, the repressilator, and studied hallmarks of the resulting nonlinear dynamics. We found that the repressilator coupled to the cell cycle shows typical quasiperiodic motion with discrete Fourier spectra and windows in parameter space with synchronization of the two oscillators, with a devil’s stair case indicating the Arnold tongues of synchronization. In the case of identical parameters for the three genes of the repressilator and simultaneous gene duplication, we identify two classes of synchronization windows, symmetric and asymmetric, depending on whether the trajectories satisfy a discrete three-fold rotation symmetry, corresponding to cyclic permutation of the three genes. Unexpectedly changing the gene doubling time revealed that the width of the Arnold tongues is connected to that three-fold symmetry of the synchronization trajectories: non-simultaneous gene duplication increases the width of asymmetric synchronization regions, for some of them by an order of magnitude. By contrast, there is only a small or even a negative effect on the window size for symmetric synchronization. This observation points to a control mechanism of synchronization via the location of the genes on the chromosome.